“Because of these modern math rules, the official correct answer today is 16.”

There is no universal modern mathematical rule that says implied multiplication must always be treated exactly the same way in every context. Different textbooks, calculators, and software have historically interpreted expressions like 8 ÷ 2(2 + 2) differently because the notation itself is ambiguous.

A more accurate explanation would be:

• Evaluate the parentheses first:

  $$8÷2(2+2)=8÷2(4)$$

• The expression is now:

  $$8÷2\times 4$$

• If multiplication and division are treated with equal precedence and evaluated left to right (the convention used in many modern textbooks and programming languages), the result is:

  $$8÷2=4,4\times 4=16.$$

• If implied multiplication $2(4)$ is interpreted as binding more tightly than division (a convention used in some older texts and by some calculators), the expression becomes:

  $$8÷(2\times 4)=8÷8=1.$$

The real mathematical lesson

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